Sliding integral proportional (SIP) controller for aircraft skid control

ABSTRACT

The sliding, integral, and proportional controller for providing aircraft antiskid braking control includes a reference velocity subsystem, a velocity error ratio subsystem, and a main controller subsystem generating a control command output signal indicative of a command braking pressure. The main controller subsystem includes a one dimensional sliding mode controller subsystem to determine an estimated net wheel torque signal, an adaptive threshold subsystem for generating an adaptive threshold based upon the modified slip ratio signal and a clock signal, integral gain subsystems, a proportional controller subsystem, and a pressure limiter. A method for determining braking efficiency of an aircraft braking system independent of the specific conditions is also provided.

RELATED APPLICATIONS

This is a continuation of Ser. No. 10/754,664, filed Jan. 8, 2004, whichis a continuation of Ser. No. 10/023,210, filed Dec. 17, 2001, now U.S.Pat. No. 6,684,147.

BACKGROUND OF THE INVENTION

This invention relates generally to aircraft landing gear brakingsystems, and more particularly concerns an improved system forcontrolling aircraft brake pressure.

A conventional skid detection system used in aircraft braking systemstypically includes a wheel speed transducer for each wheel brake of thewheels of the aircraft, for measuring wheel speed and generating wheelspeed signals that are a function of the rotational speed of the brakewheel. The wheel speed signal is typically converted to a signalrepresenting the velocity of the aircraft, and compared with a desiredreference velocity, to generate wheel velocity error signals indicativeof the difference between the wheel velocity signals from each brakedwheel and the reference velocity signal. The output of the velocitycomparator is referred to as velocity error. The velocity error signalstypically are adjusted by a pressure bias modulator (PBM) integrator, aproportional control unit, and a compensation network, the outputs ofwhich are summed to provide an anti-skid control signal received by thecommand processor. The PBM integrator in the antiskid loop dictates themaximum allowable control pressure level during braking. When no skid isdetected, this integrator allows full system pressure to the brakes.

The conventional PID controller for aircraft brake control systems dealswith various conditions such as aerodynamics, landing gear dynamics,μ-slip profile, different landing conditions, and the like. One majorproblem is that tuning of controller parameters to guarantee highefficiency in different landing conditions and conditions affecting thetire-runway coefficient of friction (μ) of the aircraft braking systemis often a difficult task.

Such algorithms usually take only one input, i.e., wheel velocity (Vw),and determine a reference velocity (Vref) with an apparatus. Then theVref and Vw signals pass through the PID control logic, which generatesa command signal. The command signal is supplied to a hydraulic servovalve and the output of servo valve, fluid pressure generates a braketorque through a brake. The algorithms show good antiskidperformance—robustness and adaptability.

In spite of success of the PID type controller, related industryengineers and researchers have been continuously investigating othercontrol schemes, partially because of difficulty in antiskid brakingcontrol parameter tuning. A need therefore still exists for an antiskidbraking controller that can facilitate and shorten the process ofantiskid braking control parameter tuning. The present invention meetsthese and other needs.

SUMMARY OF THE INVENTION

Briefly, and in general terms, the present invention provides for asliding integral proportional (SIP) controller for aircraft antiskidbraking control that improves and shortens the time required forantiskid braking control parameter tuning, and that also provides higherbraking efficiency, robustness, and adaptability, since the antiskidbraking control parameters to be tuned are adjusted based on an accurateadaptive threshold and an velocity error ratio or modified slip ratio(S_(mod)) signal with an estimated net wheel torque, a few integralgains, and a proportional gain. The proposed SIP controller requiresonly one input, and shows excellent braking efficiencies, robustness,and adaptability with only a fraction of tuning effort and time.

The present invention accordingly provides for a sliding, integral, andproportional (SIP) controller for providing anti-skid braking controlfor an aircraft. The SIP controller includes a reference velocitysubsystem generating a reference velocity signal based upon an inputwheel velocity signal; a velocity error ratio subsystem generating amodified slip ratio signal (S_(mod)) based upon a ratio of thedifference between the reference velocity and the wheel velocity to thereference velocity; and a main controller subsystem receiving thereference velocity signal and the modified slip ratio signal, andgenerating a control command output signal indicative of a commandbraking pressure.

In one embodiment, the reference velocity subsystem receives a pluralityof sampled wheel velocity signals, determines a minimum value of thesampled wheel velocity signals, and compares the minimum value with anindividual wheel velocity signal. If the minimum value of the sampledwheel velocity signals is greater than the wheel velocity signal, apredetermined desired reduction amount is subtracted from the minimumvalue of the sampled wheel velocity signals and the result is output asthe reference velocity of the reference velocity subsystem. Otherwisethe wheel velocity signal is output as the reference velocity of thereference velocity subsystem. In one aspect, the sampled wheel velocitysignals have a predetermined fixed sampling time. In a presentembodiment, the modified slip ratio signal (S_(mod)) is determined basedupon the equation:

$S_{mod} = \frac{Velerror}{Vref}$

-   -   where S_(mod) is the velocity error ratio or modified slip        ratio, Vref is the reference velocity in radians per second, and        Velerror is the velocity error in radians per second, determined        from the equation Vref−Vw, where Vw is the wheel velocity in        radians per second.

In a present embodiment, the main controller subsystem includes a onedimensional sliding mode controller subsystem to determine an estimatednet wheel torque signal; an adaptive threshold subsystem for generatingan adaptive threshold based upon the modified slip ratio signal(S_(mod)) and a clock signal; a first integral gain subsystem forcomparing the estimated net wheel torque signal with the adaptivethreshold to determine dominance between the tire drag torque andbraking torque, and outputting a corresponding gain value; a secondintegral gain subsystem exponentially generating a deep skid signal(deep_skid) when the S_(mod) signal is greater than a predeterminedlimit and a change in wheel velocity indicates a deep skid situation; athird integral gain subsystem to avoid S_(mod) signals that are toosmall or negative and to modify the initial braking command signal; aproportional controller subsystem generating an output signal to preventsudden deep skids; and a pressure limiter for limiting the commandbraking pressure. In one aspect of the invention, the output of the maincontroller subsystem is a command signal indicative of a torque, whichis converted to a command brake pressure signal by multiplication of apredetermined gain.

The estimated net wheel torque may be determined based upon the velocityestimation error. One-dimensional sliding surface condition takes a formas:

$\begin{matrix}{{\frac{1}{2}\frac{\mathbb{d}}{\mathbb{d}t}s^{2}} = {{s\frac{\partial{Vref}}{\partial t}} - {\frac{{Gain}\; 2}{{Im}\; w}{s}}}} & (1)\end{matrix}$where s=Vref−{circumflex over (V)}, Vref is the reference velocity inradians per second, {circumflex over (V)} is the observed or estimatedwheel velocity in radians per second, Gain2 is determined as the largestpossible net wheel torque in ft-lbs, and Imw is the wheel/tire/brakemass moment of inertia in slug-ft². The equation (1) is always less thanzero, and thus, the sliding condition is satisfied. The net wheel torquesignal may be determined according to the equation:

$\begin{matrix}{\frac{\partial\hat{V}}{\partial t} = {\frac{{Gain}2}{{Im}\; w}{{sgn}(s)}}} & (2)\end{matrix}$

-   -   where sgn(s) is the sign of s. The net wheel torque signal        optionally may be determined according to the equation:        NWTe=DF×sgn(s)×Gain2  (3)    -   where NWTe is the estimated net wheel torque in ft-lbs, and DF        is a discrete filter of time constant, 0.1 sec. The low pass        filter DF may be defined according to the equation:

${DF} = \frac{0.04877}{z - 0.9512}$

-   -   where z is a complex variable.

In one embodiment of the invention, a plurality of skid levels areestablished to effectively maintain a tire drag friction coefficient (μ)approaching the peak value of μ without undesirable deep skid. In onepresent aspect, three skid levels are established. Thus, for example, ifthe S_(mod) signal exceeds a first skid level threshold, the adaptivethreshold increases to a second skid level threshold to accommodate abraking torque and prevent a slip overshoot by a predetermined rate; ifthe S_(mod) signal is reduced below the second skid level threshold, thethreshold decreases to supply an appropriate braking command andmaintain the slip at the peak of μ; and the adaptive threshold becomes athird skid level threshold greater than the second skid level thresholdand the S_(mod) signal when the runway condition is very dry and tiredrag coefficient is more than a predetermined threshold drag coefficientvalue, to generate a rapid initial braking command signal. In onepresent aspect, if the tire drag coefficient value is high (more than0.5), then the rapid initial braking command signal is generated forapproximately 0–1.5 seconds period after braking is initiated.

In a present embodiment, the first integral gain subsystem outputs afirst positive gain value as the integral gain output if the estimatednet wheel torque is greater than or equal to the adaptive threshold,indicating that the tire drag torque is dominant, and outputs a secondnegative gain value as the integral gain output if the estimated netwheel torque is less than the adaptive threshold.

In another present aspect of the invention, if S_(mod) is greater thanthe deep skid limitation (Slim) of the S_(mod) signal, and if the wheelvelocity (Vw) is less than an immediately previous wheel velocity, thenthe deep skid signal (deep_skid) is determined according to thefollowing equation:deep_skid=Ta3*exp(u)  (4)

-   -   where Ta3 is the first coefficient, and is a changing negative        variable determined in a look-up table based upon the reference        velocity, and u is the S_(mod) skid level determined by the        following equation:

$u = \frac{\left( {S_{mod} - S_{\lim}} \right)}{0.01}$

In another aspect, the variable Ta3 changes to approximately zero at apredetermined reference velocity, causing an increase in the brakepressure and wheel lock-up. If the wheel velocity (Vw) is greater thanor equal to an immediately previous wheel velocity when S_(mod) isgreater than or equal to Slim, then a second positive coefficient Ta3ais substituted for Ta3. In another aspect, if S_(mod) is less than aconstant value (Sneg), and if the elapsed time from the initiation ofbraking is less than about 1 second, then the output of the thirdintegral gain subsystem is a predetermined constant, multiplied by apredetermined gain. In another present aspect, if S_(mod) is less than apredetermined maximum threshold, the output signal of the proportionalcontroller subsystem is zero.

In another present embodiment, if the product of the reference velocity(Vref) and the tire rolling radius is less than a predeterminedthreshold (Pdropout), the output signal of the proportional controllersubsystem is a predetermined constant. If the product of the referencevelocity (Vref) and the tire rolling radius is greater than or equal tothe predetermined threshold (Pdropout), then the output signal of theproportional controller subsystem is the product of the velocity errorand a predetermined negative gain. In another present aspect of theinvention, the pressure limiter limits the command braking pressurebetween about 0 and about 3000 psi.

In another present embodiment, the invention further comprises a look-uptable for converting the control command output signal indicative of thecommand braking pressure to a control command indicative of the commandcontrol current. In a present aspect, the look-up table describes anonlinear pressure vs. current relationship. In another presentembodiment, the invention further comprises a current limiter forlimiting the command control current up to about 60 mA.

The present invention also provides a method for providing sliding,integral, and proportional anti-skid braking control for an aircrafthaving a plurality of tires and brakes. An input wheel velocity signalis provided, and a reference velocity signal is generated based upon theinput wheel velocity signal. A modified slip ratio signal (S_(mod)) isthen generated based upon a ratio of the difference between thereference velocity and the wheel velocity to the reference velocity, anda control command output signal indicative of a command braking pressureis generated based upon the reference velocity signal and the modifiedslip ratio signal. In a present aspect of the method, a plurality ofsampled wheel velocity signals are provided, and a minimum value of thesampled wheel velocity signals is determined. The minimum value iscompared with individual wheel velocity signals, and if the minimumvalue of the sampled wheel velocity signals is greater than anindividual wheel velocity signal, a predetermined desired reductionamount is subtracted from the minimum value of the sampled wheelvelocity signals and the result is output as the reference velocity.Otherwise the wheel velocity signal is output as the reference velocity.In a present aspect of the method, the sampled wheel velocity signalshave a predetermined fixed sampling time.

In another aspect of the method of the invention, an estimated net wheeltorque signal is determined, an adaptive threshold is generated basedupon the modified slip ratio signal (S_(mod)) and a clock signal, theestimated net wheel torque signal is compared with the adaptivethreshold to determine dominance between the tire drag torque andbraking torque, and a corresponding first integral gain value is output.A deep skid signal (deep_skid) is exponentially generated when theS_(mod) signal is greater than a predetermined deep slid limitation(Slim) and wheel velocities indicate a deep skid situation, based uponthe modified slip ratio signal (S_(mod)), the wheel velocity signal(Vw), the reference velocity signal (Vref), the tire rolling radius, apredetermined deep skid limitation (Slim) of the S_(mod) signal, andfirst and second function coefficients. The initial braking commandsignal is modified to avoid S_(mod) signals that are too small ornegative; an output signal is generated to prevent sudden deep skids;and the command braking pressure is limited to a maximum amount.

The present invention also provides for a method for determining brakingefficiency of an aircraft braking system independent of the specificconditions. A new μefficiency (η) is determined based upon an antiskidbraking efficiency (μ_(b)), average braking force (A) of all thenon-braking forces acting to stop, or accelerate the aircraft, and theaverage braking force (B) of the aircraft braking system, according tothe following equation:

$\begin{matrix}{\eta = \frac{A + {\mu_{b} \cdot B}}{A + B}} & (6)\end{matrix}$where A is the force of all the non-braking forces acting to stop, oraccelerate the aircraft; B is the force of the aircraft braking system,and μ_(b) is the antiskid braking efficiency, determined as the actualtire drag coefficient μ divided by the peak tire drag coefficient μ.

These and other aspects and advantages of the invention will becomeapparent from the following detailed description and the accompanyingdrawings, which illustrate by way of example the features of theinvention.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic diagram of a sliding integral proportional (SIP)controller according to the present invention.

FIG. 2 is a schematic diagram of the velocity error ratio subsystem ofthe controller of FIG. 1.

FIG. 3 is a schematic diagram of the main controller subsystem of thecontroller of FIG. 1.

FIG. 4 is a schematic diagram of the sliding mode controller subsystemof the controller of FIG. 1.

FIG. 5 is a schematic diagram of the first integrator of the controllerof FIG. 1.

FIG. 6 is a schematic diagram of the second integrator of the controllerof FIG. 1.

FIG. 7 is a schematic diagram of the third integrator of the controllerof FIG. 1.

FIG. 8 is a schematic diagram of the proportional controller subsystemof the controller of FIG. 1.

FIG. 9A is a graph of the Mu (μ) vs. Slip Velocity for the aircraft B717medium landing and μ=0.5.

FIG. 9B is a graph of the Mu (μ) vs. Slip ratio for the aircraft B717medium landing and μ=0.5.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

While aircraft brake control systems typically deal with variousconditions such as aerodynamics, landing gear dynamics, μ-slip profile,different landing conditions, and the like, a major problem with the useof such controllers has been appropriate tuning of parameters for thecontroller to provide for efficient operation of such controllers indifferent landing conditions that affect the tire-runway coefficient offriction (μ) of the aircraft braking system.

As is illustrated in the drawings, the invention is embodied in asliding, integral, and proportional (SIP) controller for aircraftantiskid brake control systems that utilizes a one dimensional slidingcontroller combined with an adaptive threshold subsystem, integralgains, and a proportional gain for providing anti-skid braking control.A reference velocity signal is used as an input of a sliding modecontroller-subsystem to estimate a net wheel torque signal. A modifiedslip ratio signal (S_(mod)) is generated by a velocity error ratiosubsystem, and a deep skid signal is generated exponentially when theS_(mod) signal is greater than a given limit and wheel velocitiesindicate a deep skid situation.

The controller of the invention has been developed based onone-dimensional sliding control theory (Slotine et al., 1991) andcombined with an adaptive threshold subsystem, a few integral gains anda proportional controller.

Referring to FIG. 1, the SIP controller 20 receives only one externalinput, the wheel velocity (Vw), typically provided by a wheel speedtransducer 22 operatively connected to a wheel of an aircraft (notshown), and the reference velocity (Vref) is calculated in a referencevelocity subsystem 24 based on the wheel velocity. The referencevelocity subsystem unit takes, for example, 10 sampled signals with anappropriate fixed sampling time from the input-wheel velocity signal anda minimum value is chosen. This minimum value is compared with a wheelvelocity signal. If the value is greater than the wheel velocity signal,an appropriate reduction amount is subtracted and the result is used asa reference velocity; otherwise, the wheel velocity goes to the outputof the subsystem unit.

The wheel velocity (Vw) is subtracted from the reference velocity at asumming junction 26, resulting in a velocity error signal 28 (Velerror)which is received by a velocity error ratio subsystem 30. The velocityerror (Velerror) is measured in radians per second, and is determinedaccording to the equation:Velocity Error (rad/sec)=Vref−Vw

As is illustrated in FIG. 2, the velocity error ratio subsystemgenerates a velocity error ratio, also referred to as the modified slipratio (S_(mod)), according to the following equation:

$S_{mod} = \frac{Velerror}{Vref}$

Since the aircraft velocity signal (Vac) is not measured in the presentantiskid braking system, accurate slip (Vac−Vw) or slip ratio(Vac−Vw)/Vac are not utilized. Thus, the velocity error ratio ormodified slip ratio (S_(mod)) is calculated to obtain the adaptivethreshold and integral gains, instead.

In addition to the reference velocity subsystem and velocity error ratiosubsystem, as is illustrated in FIG. 1, the SIP controller includes amain controller subsystem 32, a look-up table #1 (34), and a currentlimiter 36 yielding the final braking command current i_(com). TheS_(mod), Vref, Vw and Velerror signals are the major inputs of the maincontroller subsystem, the output of which is the control command currenti_(com). The command pressure, P_(com) is converted to i_(com) throughthe look-up table #1, which describes a nonlinear pressure vs. currentrelationship.

Referring to FIG. 3, the main controller comprises a sliding modecontroller subsystem 38, an adaptive threshold subsystem 40, first,second and third integrator subsystems 42, 44, 46, a proportionalcontroller subsystem 48, and a pressure limiter 50. The outputs of thethree integrator subsystems are summed at a first summer 52 over aperiod defined by

$\frac{Ts}{z - 1},$where Ts is a control cycle time, and z is a complex variable. Theoutput of the proportional controller is summed with the output of thefirst summer at a second summer 54, yielding an output of the maincontroller subsystem. The output of the main controller subsystem isdimensionally torque, and is converted to a pressure signal 56 bymultiplication of Gain1 58, after which the output pressure signal(P_(com)) is limited by the pressure limiter between 0 and 3000 psi.Sliding Mode Controller

Referring to FIGS. 3 and 4, the reference velocity (rad/sec) signal isreceived by the sliding mode controller subsystem as an input forgenerating a corresponding net wheel torque(NWTe) signal (in ft-lbs.)input to the first integrator subsystem.

To design a successfully stable sliding mode controller, estimationerror vectors need to slide towards zero as quickly as possible along aseries of hyper plane intersections (Slotine et al., 1991). In thiscontroller, a one-dimensional sliding surface condition is met, becauseonly one estimation error (Ve) is obtained. The estimated net wheeltorque may be determined based upon the velocity estimation error, i.e.,Ve=V_(ref)−{circumflex over (V)}

One dimensional sliding surface condition is expressed as:

$\begin{matrix}{{\frac{1}{2}\frac{\mathbb{d}}{\mathbb{d}t}s^{2}} = {{s\frac{\partial{Vref}}{\partial t}} - {\frac{{Gain}2}{{Im}\; w}{s}}}} & (1)\end{matrix}$where s=Vref−V, Vref is the reference velocity in radians per second,{circumflex over (V)} is the observed or estimated wheel velocity inradians per second, Gain2 is determined as the largest possible netwheel torque in ft-lbs, and Imw is the wheel/tire/brake mass moment ofinertia in slug-ft².

Referring to FIG. 4, s is determined in a third summer 60 as thedifference between the reference velocity and the observed or estimatedwheel velocity, and s is input to block 62, the output of which isamplified by Gain2 at 64. The factor Gain2 is dimensionally a torque,and the equation (1) is always less than zero. Therefore, the slidingcondition is satisfied. By assessing Gain2 as the largest possibletorque, the wheel dynamics for estimating wheel velocity and NWTe may beexpressed as

$\begin{matrix}{\frac{\partial\hat{V}}{\partial t} = {\frac{{Gain}2}{{Im}\; w}{{sgn}(s)}}} & (2)\end{matrix}$where sgn(s) is the sign of s.

A discrete filter (DF) 66 of time constant, 0.1 sec, receiving theoutput of Gain2 and defined, for example, by a function such as

${{DF} = \frac{0.04877}{z - 0.9512}},$may be used as a low pass filtering means, according to the equation:NWTe=DF×sgn(s)×Gain2  (3)where NWTe is the estimated net wheel torque in ft-lbs, and DF is adiscrete filter of time constant, 0.1 sec. The estimated net wheeltorque signal is received as feedback by amplifier 68, and integratedover a period defined by block 70 to provide the observed or estimatedwheel velocity {circumflex over (V)} to summer 60.Adaptive Threshold

Referring to FIG. 3, the modified slip ratio signal (S_(mod)) and aclock signal are injected as two inputs to the adaptive thresholdsubsystem, that generates an adaptive threshold as an input to the firstintegrator subsystem.

To effectively maintain a tire drag friction coefficient (μ) at thevicinity of the peak value of μ without undesirable deep skid, threeskid levels are established such as skid-level 1, skid-level 2, andskid-level 3 in the μ vs. S_(mod) configuration. If a S_(mod) signalreaches skid-level 1 and exceeds the level, the threshold increases toaccommodate a braking torque and prevent a slip overshoot by apredetermined rate. If the S_(mod) signal is reduced below skid-level 2,the threshold decreases to supply an appropriate braking command andmaintain the slip at the peak of μ.

To generate a rapid initial braking command signal, such as when therunway condition is very dry and tire drag coefficient is high (forexample, more than 0.5), the skid-level 3 is established. The levelneeds to be a little higher than the other two skid levels and S_(mod)signal for the initial 0–1.5 seconds period after braking is initiated.

The First Integral Gain Subsystem

Referring to FIGS. 3 and 5, the output of sliding mode controller, NWTe,is compared with the adaptive threshold in the first integral gainsubsystem 42 to evaluate dominance between the tire drag torque andbraking torque. Once the dominance is evaluated, a corresponding gainvalue (T_(apply)) is determined as the output of the subsystem. Forexample, if NWTe is greater than the adaptive threshold, that is, thetire drag torque is dominant, then a positive gain value Ta1 goes tooutput of the subsystem; if NWTe is less than the adaptive threshold, inother words the braking torque is being applied excessively, then anegative gain value Ta2 is supplied as an integral gain.

Although only one of two gains is determined in the subsystem throughthe evaluation of torque dominance using the adaptive threshold, thesystem operates to modulate a pressure bias.

The Second Integral Gain Subsystem

Referring to FIGS. 3 and 6, the inputs of the second integral gainsubsystem are S_(mod), Vw, Vref, r_r (the tire rolling radius in ft),Slim (the deep skid limitation in μ vs. S_(mod) configuration), a firstcoefficient Ta3, and a second coefficient Ta3a. The output is a deepskid signal (deep_skid).

Referring to FIG. 9B, when the abscissa of vertex of accurate μ vs. slipratio is 0.056, the corresponding S_(mod) limitation may be chosen as0.038 and this skid limitation is termed as Slim here. If the S_(mod) isgreater than this limitation and Vw is less than Vw_prv (previous Vw),then the deep skid signal is released by the exponential function #1.Function #1: deep_skid=Ta3*exp(u)  (4)where

$u = \frac{\left( {{S\;{mod}}\mspace{11mu} - {S\;\lim}}\; \right)}{0.01}$

The deep skid (DS) signal amplifies exponentially depending on theS_(mod) skid level, u. Furthermore, Ta3 is not a constant but a changingnegative variable along the reference velocity, which is determined in alook-up table #2 72. The coefficient Ta3 is a variable that changes toapproximately zero at a certain Vref level (P_dropout), i.e., Ta3=0, ifVref≦P_dropout. This causes the brake pressure increase and wheellock-up, when the Vref reaches the P_dropout.

In anti-skid control, the wheel velocity is often quite close to theaircraft velocity immediately after a large decrease in brake pressure,which may result in a low braking efficiency. To remedy this, the wheelvelocity (Vw) is monitored in discrete intervals, with the wheelvelocity (Vw) of a given interval being compared with a wheel velocityVw_prv of an immediately previous interval, under the condition ofS_(mod)≧Slim. If Vw is greater than or equal to Vw_prv, then a differentpositive coefficient Ta3a is incorporated into the exponential function#2.Function #2: deep_skid=Ta3a*exp(u)  (5)The Third Integral Gain Subsystem

Referring to FIGS. 3 and 7, to avoid S_(mod) signals that are too smallor negative, a simple logic is utilized in the third integral gainsubsystem, illustrated in the flow diagram of FIG. 7. If S_(mod) is lessthan a constant value (Sneg), then the output skid_neg=Ta0. Ta0 is apredetermined constant. To enhance the initial braking command signalwithin about 0 to 1.0 second, one device is needed besides theadjustment of skid_level3 of the adaptive threshold subsystem, that is,the constant Ta0 is multiplied by a gain (enhance_init), and thus anoutput signal (Skid_neg) is generated by the third integral gainsubsystem.

The Proportional Controller

Referring to the flow chart illustrated in FIG. 8, a proportionalcontroller 48 is incorporated into the SIP controller to prevent suddendeep skids, which are often observed in aircraft antiskid brakingsimulations and flight test data, even under constant μ runwayconditions.

One feature of the proportional controller that is different from aconventional proportional controller is that the proportional controlaction occurs only when the Vref is above a certain level (Pdropout). Ifthe Vref reaches Pdropout and proceeds below it, then the output changesto a constant value (T_p0), and this also helps a necessary rapid wheellock-up near dead stop as the coefficient Ta3 drops to zero in the thirdintegral gain subsystem.

FIGS. 9A, and 9B illustrate some antiskid physics obtained for theaircraft B717 medium landing and μ=0.5. FIG. 9A demonstrates that thetire-runway coefficient of friction (μ) changes as the aircraft slipvelocity decreases. The peak μ is located around the slip velocity of12.5 ft/sec. However, from FIG. 9B it can be seen that the μ vs. slipratio curve does not vary significantly during the braking and aircraftdeceleration. From FIGS. 9A and 9B, it may be observed that the SIPcontroller manages antiskid performance near the peak μ (0.5) or frontside of the curves well. In FIG. 9B, the peak u is found at the slipratio of about 0.056.

For the main landing gear dynamic model, two D.O.F. nonlinear lagrangianequations based on a T-shape gear configuration are incorporated in theSimulation model. The Simulation shows a close correlation between thebrake torque and gear walk stability. It is noted that sudden drops ofbrake torque amplifies slightly the gear walk velocity.

The SIP controller of the invention has been tested for broad range oftire-runway friction coefficients for B717 parameters in a non real timeenvironment. The simulation results show high efficiency, i.e, 97.4% forMumax=0.1, 94.3% for Mumax 0.5, 92.4% for Mu-step 0.4–0.2. The dynamicmodel of aircraft, wheel, main and nose landing gears, hydraulic system,torque data, and aerodynamic models have been carefully examined andincorporated in the closed loop control model to test the SIP controllerand to evaluate antiskid performance.

The main landing gear stability has been also tested with an externalpulse force by the assumption that fore-aft gear damping ratio=0 and upto −15% of critical damping. Very excellent damping effects have beenobserved even for −15% damping ratio under the condition that ahorizontal axle acceleration would be available and added to the controlsignal output.

The simulations have been performed for the B717 aircraft parameters,T-shape main landing gears, a hydraulic system, and brakes in a non realtime environment.

The simulation results show a successful performance with highefficiencies for various tire drag friction coefficients (μ) with only afew tuning parameters.

TABLE 1 Braking Efficiency, B717 Medium Landing μ Efficiency* 0.1 97.4%0.5 94.3% Stepped μ0.4–0.2 92.4%

In table 1, the Efficiency* is a higher efficiency by comparison amongthe cumulative distance efficiency and new μ efficiency, explainedbelow.

Braking Performance

The New μ Efficiency Method:

The new μ efficiency (η) of the present invention, and cumulativedistance efficiency (described in the Hydro-Aire Default Simulation PlanR 1397) are interrelated for any set of conditions.

$\begin{matrix}{\eta = \frac{A + {\mu_{b} \cdot B}}{A + B}} & (6)\end{matrix}$

-   -   where A is the average braking force of all the non-braking        (i.e. aerodynamic) forces that are acting to stop, or accelerate        the aircraft, the main factors of which are flaps, spoilers,        body drag, thrust reversers, wind, runway slope, and the like; B        is the average braking force assuming the braking is perfect;        and μ_(b) is the antiskid braking efficiency, actual μ divided        by the peak μ.

In this way, the braking performance is calculated independent of thespecific conditions. The new μ efficiency method shows a lowerefficiency as the overall efficiency decreases, especially for theμ-step tire runway condition. However, the higher the efficiency, thesmaller the difference.

Gear Stability with a Horizontal Component of Wheel Axle Acceleration:

It should be appreciated that if a wheel axle acceleration signal isavailable in future, the horizontal component of acceleration multipliedby a gain can be directly added to the control current output signal,which can increase the overall closed loop damping effect of the systemdramatically. Excellent gear stability is expected even for negativevalue of fore-aft landing gear damping up to 15% of the critical dampingratio.

It will be apparent from the foregoing that while particular forms ofthe invention have been illustrated and described, various modificationscan be made without departing from the spirit and scope of theinvention. Accordingly, it is not intended that the invention belimited, except as by the appended claims.

1. A sliding, integral, and proportional controller for providinganti-skid braking control for an aircraft having a plurality of tiresand brakes, comprising: a reference velocity subsystem generating areference velocity signal based upon an input wheel velocity signal;means for generating a velocity error signal based upon the referencevelocity signal and the input wheel velocity signal; a velocity errorratio subsystem generating a modified slip ratio signal (S_(mod)) basedupon a ratio of the difference between the reference velocity and thewheel velocity to the reference velocity; a main controller subsystemreceiving the reference velocity signal and the S_(mod) signal, the maincontroller subsystem generating a control command output signalindicative of a command braking pressure responsive to the referencevelocity signal and the S_(mod) signal, the main controller subsystemincluding: a) a one dimensional sliding mode controller subsystem todetermine an estimated net wheel torque signal; b) an adaptive thresholdsubsystem for generating an adaptive threshold based upon the S_(mod)signal and a clock signal; c) first summing means for summing anintegral gain, a deep skid signal, and a modification of an initialbraking command signal to avoid S_(mod) signals that are too small ornegative of an initial braking command signal to provide an output sum,said integral gain being based upon the estimated net wheel torquesignal and the adaptive threshold, and said deep skid signal being basedupon the S_(mod) signal, the wheel velocity signal, the referencevelocity signal, a tire rolling radius, a predetermined deep skidlimitation of the S_(mod) signal, and first and second functioncoefficients; and d) a proportional controller subsystem generating aproportional controller output signal to prevent sudden deep skids basedupon said S_(mod) signal and said velocity error signal; and e) secondsumming means for summing said output sum and said proportionalcontroller output signal to provide said control command output signal.2. The sliding, integral, and proportional controller of claim 1,wherein the control command output signal of the main controllersubsystem is a torque.
 3. The sliding, integral, and proportionalcontroller of claim 2, wherein the control command output signal isconverted to a command brake pressure signal by multiplication of saidcontrol command output signal by a predetermined gain.
 4. A method forproviding sliding, integral, and proportional anti-skid braking controlfor an aircraft having a plurality of tires and brakes, comprising:providing an input wheel velocity signal; generating a referencevelocity signal based upon the input wheel velocity signal; generating avelocity error signal based upon the reference velocity signal and theinput wheel velocity signal; generating a modified slip ratio signal(S_(mod)) based upon a ratio of the difference between the referencevelocity and the wheel velocity to the reference velocity; anddetermining an estimated net wheel torque signal; generating an adaptivethreshold based upon the S_(mod) signal and a clock signal; summing anintegral gain, a deep skid signal, and a modification of an initialbraking command signal to avoid S_(mod) signals that are too small ornegative of an initial braking command signal to provide an output sum,said integral gain being based upon the estimated net wheel torquesignal and the adaptive threshold, and said deep skid signal being basedupon the S_(mod) signal, the wheel velocity signal, the referencevelocity signal, a tire rolling radius, a predetermined deep skidlimitation of the S_(mod) signal, and first and second functioncoefficients; generating a proportional controller output signal basedupon said S_(mod) signal and said velocity error signal; and summingsaid output sum and said proportional controller output signal toprovide said control command output signal.
 5. The method of claim 4,wherein the control command output signal is a torque.
 6. The method ofclaim 5, wherein the control command output signal is converted to acommand brake pressure signal by multiplication of the control commandoutput signal by a predetermined gain.